Contents
How to determine equal or unequal variance in t tests?
1. Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test. Sample 1 has a variance of 24.86 and sample 2 has a variance of 15.76.
How to test the null hypothesis for the variance?
We will test the null hypothesis that the true variance is equal to 0.01. H0: σ2= 0.01 Ha: σ2≠ 0.01 Test statistic: T= 0.3903 Degrees of freedom: N- 1 = 99 Significance level: α= 0.05 Critical values: Χ 2α/2,N-1= 73.361 Χ 21-α/2,N-1= 128.422 Critical region: Reject H0if T 73.361 or T> 128.422
How to test the hypothesis that population means are equal?
We are testing the hypothesis that the population means are equal for the two samples. We assume that the variances for the two samples are equal. H0: μ1= μ2Ha: μ1≠ μ2
How to test the variance of a distribution?
Based on Theorem 2 of Chi-square Distribution and its corollaries, we can use the chi-square distribution to test the variance of a distribution. Example 1: A company produces metal pipes of a standard length.
Can a t-test be run on an unequal sample size?
Theoretically, if the assumption of equal variances is satisfied and the dependent variable is normally distributed you could run a t-test despite the unequal sample sizes between the two comparison groups. I suggest you read these two posts ( 1 & 2) which deal with similar issues.
What are the variables in the t test?
A number of different variables were measured (departure date, arrival date, duration of migration etc.) so there are multiple tests, some of which the variances are very different (the smaller sample having higher variance).
When to use normal distribution or two sample t test?
For this approach to give valid results it is important that people be assigned to each group at random. Such samples are independent. When the population variances are known, hypothesis testing can be done using a normal distribution, as described in Comparing Two Means when Variances are Known. But population variances are not usually known.